the open box problem

This is a discussion on the open box problem within the A Brief History of Cprogramming.com forums, part of the Community Boards category; lo.
Being a general retard, I am having difficulty with my coursework, and the deadline grows ever nearer.
The problem ...

The main aim of this activity is to determine the size of the square cut which makes the volume of the box as large as possible for any given rectangular sheet of card.

Part one
For any sized square sheet of card, investigate the size of the cut out square which makes an open box of the largest volume.

Part two
For any sized rectangular sheet of card, investigate the size of the cut out square which makes an open box of the largest volume.

You may do practical work and/or work in symbols.
Your teacher will help you choose the best way of working on the problem

I'm not expecting you to do my homework for me, but it would be extremely helpful if you could point me in the right direction.

I have done:
I have figured out the formula for working out the volume for the dimensions:
cutoffwidth * (lengthofcard - 2 * cutoffwidth) * (widthofcard - 2 *cutoffwidth)

and I have discussed how to calculate the formula for finding a square piece of cards' optimal cutoff width from it's dimensions, which is:
Optimal Cutoff Width of Square = Square's Width (or length) / 6

being mentally handicapped when it comes to mathematics, I am stuck on the bit which involves working out how to find the optimal cutoff width for a rectangle. The only method I have been able to employ so far is brute force.

Hope at least one of you has understood that.
Furthermore, I hope that person can help.

this is a question of a maximum (extrema? I don't remember what they called it) Your function of volume is a function of the length of a side of the cut out boxes. simply calculate the maximum on the graph.

there's probably a more basic way but I know this can be done with a little basic calc. simply derive and find out where the f'(x) is 0.

if w=width of card, l=length of card, and x is the size of the box you are cutting out, then this is the equation:

x*(l-2x)*(w-2x)=y

To solve, you can graph this equation with l and w being whatever value you want, and your answer is where the graph is maximum and positive. The other way (and its been awhile since I've done this so I might be a little wrong) is to take the derivitive of the above equation for any value of w and l, set it equal to zero, and solve for x, and this should be your maximum as well.

Thanks for the help so far. A friend of mine will be helping me with this, for now I'll just plot a few meaningless graphs to make it look like I've done work, and I might see a pattern in the mean time.

"Owners of dogs will have noticed that, if you provide them with food and water and shelter and affection, they will think you are god. Whereas owners of cats are compelled to realize that, if you provide them with food and water and shelter and affection, they draw the conclusion that they are gods."
-Christopher Hitchens

"Owners of dogs will have noticed that, if you provide them with food and water and shelter and affection, they will think you are god. Whereas owners of cats are compelled to realize that, if you provide them with food and water and shelter and affection, they draw the conclusion that they are gods."
-Christopher Hitchens